Acronym	quitit
Name	quasitruncated tesseract
Cross sections	©
Circumradius	sqrt[(5-3 sqrt(2))/2] = 0.615370
Inradius wrt. quith	[sqrt(2)-1]/2 = 0.207107
Inradius wrt. tet	(4-3 sqrt(2))/4 = 0.060660
Density	15
Coordinates	((sqrt(2)-1)/2, (sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2)   & all permutations, all changes of sign
Volume	(72 sqrt(2)-101)/6 = 0.137229
Surface	56-36 sqrt(2) = 5.088312
General of army	sidpith
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: quith tet quitit 8 16 )
Face vector	64, 128, 88, 24
Confer	blends: otbaquitit   general polytopal classes: Wythoffian polychora   analogs: quasitruncated hypercube qtCn
External links

As abstract polytope quitit is isomorphic to tat, thereby replacing the octagrams by octagons, resp. replacing quith by tic.

Note that the tets become retrograde here.

Incidence matrix according to Dynkin symbol

o3o3x4/3x

. . .   . | 64 |  3  1 |  3  3 |  1 3
----------+----+-------+-------+-----
. . x   . |  2 | 96  * |  2  1 |  1 2
. . .   x |  2 |  * 32 |  0  3 |  0 3
----------+----+-------+-------+-----
. o3x   . |  3 |  3  0 | 64  * |  1 1
. . x4/3x |  8 |  4  4 |  * 24 |  0 2
----------+----+-------+-------+-----
o3o3x   . ♦  4 |  6  0 |  4  0 | 16 *
. o3x4/3x ♦ 24 | 24 12 |  8  6 |  * 8

o3o3/2x4/3x

. .   .   . | 64 |  3  1 |  3  3 |  1 3
------------+----+-------+-------+-----
. .   x   . |  2 | 96  * |  2  1 |  1 2
. .   .   x |  2 |  * 32 |  0  3 |  0 3
------------+----+-------+-------+-----
. o3/2x   . |  3 |  3  0 | 64  * |  1 1
. .   x4/3x |  8 |  4  4 |  * 24 |  0 2
------------+----+-------+-------+-----
o3o3/2x   . ♦  4 |  6  0 |  4  0 | 16 *
. o3/2x4/3x ♦ 24 | 24 12 |  8  6 |  * 8

o3/2o3x4/3x

.   . .   . | 64 |  3  1 |  3  3 |  1 3
------------+----+-------+-------+-----
.   . x   . |  2 | 96  * |  2  1 |  1 2
.   . .   x |  2 |  * 32 |  0  3 |  0 3
------------+----+-------+-------+-----
.   o3x   . |  3 |  3  0 | 64  * |  1 1
.   . x4/3x |  8 |  4  4 |  * 24 |  0 2
------------+----+-------+-------+-----
o3/2o3x   . ♦  4 |  6  0 |  4  0 | 16 *
.   o3x4/3x ♦ 24 | 24 12 |  8  6 |  * 8

o3/2o3/2x4/3x

.   .   .   . | 64 |  3  1 |  3  3 |  1 3
--------------+----+-------+-------+-----
.   .   x   . |  2 | 96  * |  2  1 |  1 2
.   .   .   x |  2 |  * 32 |  0  3 |  0 3
--------------+----+-------+-------+-----
.   o3/2x   . |  3 |  3  0 | 64  * |  1 1
.   .   x4/3x |  8 |  4  4 |  * 24 |  0 2
--------------+----+-------+-------+-----
o3/2o3/2x   . ♦  4 |  6  0 |  4  0 | 16 *
.   o3/2x4/3x ♦ 24 | 24 12 |  8  6 |  * 8